 Hello and welcome to this session. In this session we discuss about reflection. We often see our image in mirror or water. We call it reflection. So our reflection or flip is a transformation where each point in our shape appears at an equal distance on opposite side of a given line and this is called the line of reflection. Reflection creates a mirror image of the original figure. In this picture the red line is the line of reflection. Now we discuss reflection in x-axis and y-axis. First let us study reflection in x-axis and we know that in reflection the point and its image are at the same distance from the line of reflection. For example let us consider a point A with the coordinates 2,1. It will lie in the first quadrant. Let us plug it on the coordinate plane. Here we have point A and we see that this point is one unit above x-axis and if we have to see its image in x-axis then this point must be at the distance of one unit below x-axis and will lie exactly below this point on the same line. So we plot it here and level it as A prime. Now we see that the coordinates of the point A prime are 2-1. Here we see that the x-coordinate remains same and y becomes negative. Mathematically we can say that if we coordinate x-y changes to x-y and reflection in x-axis that is we multiply y-coordinate with minus 1 and x-coordinate remains same. In this graph we see that point A has coordinates 2,1 and its image in x-axis that is point A prime has the coordinates 2 minus 1. Now let us study reflection in y-axis. Again we know that in reflection the point and its image at the same distance from the line of reflection for example let us consider the same point A with the coordinates 2,1. It lies in the first quadrant. We can see this point is at the distance of two units from y-axis. If we have to see its image in y-axis then this point must be at a distance of two units from y-axis but on the other side of y-axis and will lie exactly on the same horizontal line. So we plot it here and name it as A double prime. Now we see that the coordinates of image A double prime are minus 2,1. Here y-coordinate remains same and x becomes negative. So we can say that here the coordinates x-y changes to minus x-y and reflection in y-axis. That is we only multiply x-coordinate with minus 1 and y-coordinate remains same. That is in the graph we see that point A with the coordinates 2,1 has its image in y-axis that is point A double prime with the coordinates minus 2,1. Now we are going to discuss reflection in line y is equal to x. We know that y is equal to x is a straight line passing through origin that is 00. So here we have a straight line passing through origin and given by the equation y is equal to x. Now again we consider the point A with the coordinates 2,1 and we will find its reflection along the line y is equal to x. First we plot this point A on the coordinate plane and here we get the required point and when we plot its reflection in y is equal to x it will be 1,2. We label it as A prime. Here we see that the coordinates into change that is x-y changes to y-x image of point A with the coordinates 1,2 will be A prime with the coordinates 2,1. Here is the point A with the coordinates 2,1 and its image along the line y is equal to x is given by A prime with the coordinates 1,2. So if you have to find reflection of any figure like triangle, quadrilateral, etc. We first find the image of each vertex in the coordinate plane using the above mentioned methods of plotting points in the coordinate plane and then we join the new points and get the required image. This completes our session but we enjoyed this session.